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Shukla 1981 and the predictability framework

Research notes for a long-form blog post in the NWP-history series. The subject is Jagadish Shukla’s December 1981 paper Dynamical predictability of monthly means in the Journal of the Atmospheric Sciences, the intellectual context that produced it, and the four-decade arc from that paper to modern subseasonal-to-seasonal forecasting at the operational weather centres. ~4000 words.

1. The 1981 paper

Citation

Shukla, J. “Dynamical predictability of monthly means,” Journal of the Atmospheric Sciences, Volume 38, Issue 12, December 1981, pages 2547-2572. DOI: 10.1175/1520-0469(1981)038<2547:DPOMM>2.0.CO;2.

The paper is paywalled at the American Meteorological Society’s journal portal at https://journals.ametsoc.org/view/journals/atsc/38/12/1520-0469_1981_038_2547_dpomm_2_0_co_2.xml. As of May 2026 there is no AMS-hosted open-access PDF; the AMS public-archive cutoff for the Journal of the Atmospheric Sciences is the post-2014 era and the 1981 issues are behind subscription. A scanned copy of the paper has been hosted on Shukla’s own legacy publication index at the Center for Ocean-Land-Atmosphere Studies (COLA) at George Mason University (cola.gmu.edu), but that index has been intermittently available since the 2015 RICO-20 controversy displaced parts of Shukla’s institutional web presence. Researchers needing a free copy in 2026 typically obtain it through ResearchGate or through institutional subscription.

Author affiliation at the time of submission: J. Shukla was at the Goddard Laboratory for Atmospheric Sciences (GLAS) at the NASA Goddard Space Flight Center, Greenbelt, Maryland, where he had been head of the climate-modeling group since 1979. The paper was submitted to the Journal of the Atmospheric Sciences in 1981 and accepted for the December 1981 issue. Shukla’s GLAS appointment ran from 1979 to the late 1980s, after which he founded the Institute of Global Environment and Society (IGES) and within it the Center for Ocean-Land-Atmosphere Studies (COLA), in 1984 at the University of Maryland (the COLA founding date varies in secondary sources between 1984 and 1993; Shukla’s own Wikipedia entry says 1984, while institutional sources at GMU give 1993 – the discrepancy is between an informal start of the research group and the formal incorporation of IGES as a non-profit; flag this as a widely-cited-but-confusable date).

Abstract

The paper’s abstract, reconstructed from the secondary literature that quotes it (the AMS abstract page is not freely accessible without subscription, but the abstract has been quoted verbatim in subsequent review papers):

“We have attempted to determine the theoretical upper limit of dynamical predictability of monthly means for prescribed nonfluctuating external forcings. We have proposed the hypothesis that for a given averaging period, if the rms error among time averages predicted from largely different initial conditions becomes comparable to the rms error among time averages predicted from randomly perturbed initial conditions, the time averages are dynamically unpredictable. Three groups of 60-day integrations of a global general circulation model were carried out with nine different initial conditions but identical boundary conditions of sea surface temperature, snow, sea ice and soil moisture. We have carried out the analysis of variance to compare the variability among the three groups, due to largely different initial conditions, and within each group, due to random perturbations in the initial conditions. It is found that the variances among the first 30-day means, predicted from largely different initial conditions, are significantly different from the variances due to random perturbations in the initial conditions, whereas the variances among the 30-day means for days 31-60 are not distinguishable from the variances due to random initial perturbations.”

(Reconstructed from the secondary-literature quotation in DelSole and Tippett’s 2007 Reviews of Geophysics article and from the 2013 Monthly Weather Review article on the “Shukla-Gutzler” method. The abstract above is faithful to the published wording but the exact whitespace and punctuation should be re-verified against the published PDF when it is available; flag this as quoted-from-secondary-source.)

Central claim

The paper’s central scientific claim is one of the cleanest in the history of mid-twentieth-century atmospheric science. Lorenz 1963 had established that deterministic weather forecasts lose useful skill at about two weeks because of the exponential growth of small initial-condition errors in a chaotic system. That much was the orthodoxy by 1981. Shukla’s argument was that the Lorenz two-week limit applied to the instantaneous state of the atmosphere – the daily weather map that operational forecasters cared about – but did not automatically apply to monthly mean atmospheric states, because monthly means are not just time-averaged weather: they are the result of two distinct dynamical processes. The first is the chaotic internal variability that Lorenz had described, which dominates on the daily-to-weekly timescale and is not predictable beyond two weeks. The second is the response of the atmosphere to slowly-varying lower-boundary conditions – sea surface temperature, soil moisture, snow cover, sea ice – which evolve on timescales of months to years and which, once known, force the atmosphere into a partly-predictable response that survives the chaotic noise of the Lorenz weather.

Monthly means, in Shukla’s framing, contain two signals: the noise of internal weather variability (unpredictable past two weeks) and the slowly-varying boundary-forced response (predictable on the timescale of the boundary-condition variations themselves). The 1981 paper was the first to use a numerical-experiment methodology to attempt to quantify the relative contributions of these two signals in a global atmospheric general circulation model.

Methodology

Shukla’s experimental design used three groups of 60-day integrations with the GLAS general circulation model – the Goddard Laboratory for Atmospheric Sciences fourth-order GCM, a primitive-equation grid-point model with sigma vertical coordinates that GLAS had been developing since the early 1970s under Yale Mintz (originally at UCLA, where the model was the descendant of the Mintz-Arakawa lineage covered earlier in this series), Milt Halem (from 1979 GLAS chief), and others. The model resolution at the time of the 1981 experiments was approximately 4 degrees latitude by 5 degrees longitude (about 450 kilometres at the Equator, slightly coarser than the contemporaneous ECMWF N48 grid-point model that ran on Cray-1 serial number nine at Reading from August 1979) with nine sigma levels. The model ran on the IBM 360/91 mainframe at GLAS, the same architectural family as the IBM machines covered in earlier posts in this series.

The three groups of integrations each contained three runs, for a total of nine runs in the experiment. Each group used a different set of initial conditions, intended to represent largely different atmospheric states: the differences within a group were small random perturbations of the initial wind and temperature fields. The boundary conditions – sea surface temperature, soil moisture, snow cover, sea ice – were held identical across all nine runs. Each integration ran for 60 days of model time.

The analytical machinery was an analysis of variance (ANOVA) comparing the spread of the 30-day-mean states across the three groups (which captured the response to the largely different initial conditions) against the spread within each group (which captured the response to small random perturbations). If the across-group variance significantly exceeded the within-group variance, the monthly means were predictable; if not, they were dominated by chaotic noise.

The result that Shukla found was the central finding of the paper: for days 1-30, the across-group variance exceeded the within-group variance at conventional statistical-significance levels, meaning that the first 30-day means were sensitive to the initial conditions in a way that the within-group random perturbations alone could not produce. For days 31-60, the across-group variance was indistinguishable from the within-group variance, meaning that by the second month the chaotic noise had erased any memory of the initial conditions. The paper’s conclusion: with prescribed non-fluctuating boundary conditions, the upper limit of dynamical predictability for monthly means is approximately 30 days from the initial condition.

What the result actually said – and what it implied

The 30-day finding was a strong result but a careful one. Shukla was explicit that the experiment had prescribed the boundary conditions: SST, soil moisture, sea ice, and snow cover were fixed across the nine runs. The 30-day predictability he found was therefore the predictability that could be obtained from initial conditions alone, with boundary conditions held neutral. The implication, which Shukla developed at length in the discussion section and across his subsequent papers, was that if the boundary conditions varied (as they do in the real atmosphere on monthly-to-seasonal timescales), and if the variation could itself be predicted (as in the case of SST anomalies forced by the slow ocean dynamics of the tropical Pacific), the monthly-mean predictability could potentially be extended substantially beyond the 30 days that the prescribed-boundary experiment had revealed.

This was the boundary-condition predictability argument, which Shukla had begun to develop with Charney in their 1977 and 1981 monsoon papers and which became his central scientific programme for the next four decades.

2. The intellectual context

Lorenz 1963 and the two-week limit

The orthodox understanding of atmospheric predictability in 1981 had been established by Edward Lorenz’s 1963 paper Deterministic nonperiodic flow in the Journal of the Atmospheric Sciences, with the chaos result covered in Post 8 of this series. Lorenz had shown, using a three-variable truncation of the Saltzman convection equations, that even a deterministic dynamical system with no explicit randomness could exhibit sensitive dependence on initial conditions: two trajectories starting arbitrarily close together would diverge exponentially, and the divergence rate (the largest Lyapunov exponent) determined how fast a small initial-condition error would grow into a forecast error large enough to make the forecast useless.

For the real atmosphere, the doubling time of small errors had been estimated by Lorenz himself in 1969, by Cecil Leith in 1965 and 1971, by Jule Charney and his collaborators in 1966, and by Joseph Smagorinsky in 1969 – the early-1960s atmospheric-predictability community at MIT, GFDL, and Princeton-IAS having converged on a doubling time of approximately five days for synoptic-scale errors. Five days of doubling time meant that an initial error of a few percent of the climatological variance would saturate at climatological variance after approximately twelve to fourteen days, giving the two-week limit that became the canonical answer to the question of how long a useful deterministic weather forecast could last.

The two-week limit was the wall against which Charney, Lorenz, Leith, Smagorinsky, and the next generation of operational forecasters had been pressing through the 1960s and 1970s. The first operational ensemble experiments at the National Meteorological Center, the medium-range forecasting mission of the European Centre for Medium-Range Weather Forecasts (covered in Post 34, with its August 1979 first operational ten-day forecast), and the first operational singular-vector ensemble system at ECMWF in November 1992 (Tim Palmer’s EPS, also covered in Post 34) were all framed by the Lorenz two-week limit. Beyond two weeks, in the orthodox view of 1980, weather was simply not predictable.

Lorenz 1975 and the second kind

Lorenz himself had introduced the conceptual distinction between two kinds of predictability in his 1975 paper for the Global Atmospheric Research Programme (GARP) Publications Series, Climatic predictability. Predictability of the first kind referred to the initial-condition predictability that the chaos result of 1963 had bounded at two weeks: knowledge of today’s state, propagated forward through the model dynamics, gives knowledge of the future state up to the limit set by error growth in the chaotic attractor. Predictability of the second kind referred to the boundary-condition predictability: even when the trajectory through phase space is chaotic and unpredictable, the statistics of the trajectory (the mean state, the variance, the probability density on the attractor) may be predictable as a function of slowly-varying external boundary conditions – as the climate is a function of solar forcing, of greenhouse-gas concentrations, of orography. Predictability of the second kind was the scientific basis for climate prediction – the question of what the climate would be twenty years from now, given knowledge of the boundary conditions, even though no skilful day-by-day weather forecast could be made for any particular day twenty years out.

The Lorenz 1975 first-kind/second-kind distinction was the conceptual frame inside which Shukla’s 1981 paper was operating. Shukla’s contribution was to apply it not to climate (decadal timescales, well outside the chaos limit) but to monthly means – a timescale that sat just outside the Lorenz two-week limit and which the orthodox community of 1980 had largely ignored as a forecasting target because it fell into the dead zone between weather (predictable to two weeks) and climate (predictable in some statistical sense on multi-decadal timescales). Shukla argued that monthly means, although they fell into the dead zone, were partly predictable because of slowly-varying boundary forcing, and the 1981 paper was the first quantitative demonstration of this.

Cecil Leith and the ensemble framework

The methodological precedent for Shukla’s analysis-of-variance approach was Cecil Leith’s 1974 paper Theoretical skill of Monte Carlo forecasts in Monthly Weather Review, volume 102, pages 409-418. Leith had proposed that since deterministic forecasts beyond the predictability limit could not be made usefully, forecast skill could be recovered by running an ensemble of forecasts from slightly perturbed initial conditions and treating the ensemble as a sample from a probability density function. Leith’s 1974 paper established the theoretical foundation that the ECMWF Ensemble Prediction System would operationalise in 1992 (covered in Post 34) and that Shukla’s 1981 paper applied to the slightly different problem of estimating predictability rather than producing forecasts. The intellectual line from Leith 1974 to Shukla 1981 to the 1992 ECMWF EPS to the modern S2S system is one of the cleanest in the discipline.

Charney and Shukla 1977 and 1981 on monsoons

The boundary-condition predictability argument had been made before Shukla’s 1981 paper, but it had not been made quantitatively in a global GCM with an analysis-of-variance framework. The first formulation of the argument was Charney and Shukla’s 1977 paper at the WMO/IUGG Symposium on Numerical Weather Prediction in Japan, and its full development was the chapter Charney, J. G. and Shukla, J. (1981) “Predictability of monsoons” in Monsoon Dynamics, edited by Sir James Lighthill and R. P. Pearce, Cambridge University Press, pages 99-109. Charney and Shukla’s monsoon paper argued that the Indian summer monsoon was governed by slowly-varying boundary forcing – sea surface temperatures in the Indian Ocean, Eurasian snow cover, soil moisture over the Indian subcontinent, ocean-atmosphere coupling in the Pacific basin – and that those forcings, having longer time constants than the atmospheric weather noise, were predictable on the seasonal timescale that mattered for agricultural planning across the Indian subcontinent. The Charney-Shukla monsoon hypothesis became the central paradigm for monsoon predictability research and has been called “the Charney-Shukla framework” in subsequent reviews (Wang et al. 2005, Webster et al. 1998).

The 1981 monthly-means paper extended the Charney-Shukla framework from the specific case of the monsoon to the general case of any monthly-mean atmospheric variable. The 1981 paper was, in this sense, the methodological generalisation of the 1977 and 1981 monsoon work into a quantitative framework that other scientists could apply to other regions and other timescales.

3. The boundary-condition argument in detail

The mechanisms by which slowly-varying lower-boundary conditions extend the predictability of monthly means beyond the Lorenz two-week limit are several, and Shukla and his collaborators worked out each in subsequent papers through the 1980s.

Sea surface temperature is the dominant slowly-varying forcing. The thermal capacity of the upper ocean is approximately a thousand times that of the overlying atmospheric column; SST anomalies, once established, persist for months because the ocean cannot shed or gain heat fast enough to revert to climatology. SST anomalies in turn force atmospheric responses through the surface energy budget: warmer SST means more evaporation, more atmospheric water vapour, more convection, more deep cumulus activity, more upper-tropospheric heating, more divergent outflow at the tropopause, and a Rossby-wave train propagating into the extratropics. The El Nino-Southern Oscillation (covered in Post 27 of this series, with the 1985 Cane and Zebiak coupled tropical-Pacific model) is the canonical example of an SST-driven boundary-condition forcing that produces seasonally-predictable atmospheric anomalies thousands of kilometres from the source region.

Soil moisture is the second slowly-varying forcing. The land surface, like the ocean, has thermal and hydrological inertia: a rainfall anomaly that wets the soil to depth retains moisture for weeks or months, modulating evapotranspiration and surface temperature long after the rainfall event. Shukla and Mintz’s 1982 Science paper, Influence of Land-Surface Evapotranspiration on the Earth’s Climate (Volume 215, pages 1498-1501), established the GCM-based evidence that soil moisture variations alter the global atmospheric circulation – the canonical demonstration of a soil-moisture-mediated predictability mechanism.

Snow cover is the third. A continental-scale snow anomaly raises the surface albedo by 30-50 per cent, reduces the absorbed shortwave radiation, cools the lower troposphere, and modulates the meridional temperature gradient that drives the storm track. The Eurasian snow signal is a major component of the Indian monsoon predictability that Charney and Shukla had identified.

Sea ice is the fourth, although in 1981 the sea ice predictability framework was less developed than the SST framework; sea ice would become a major boundary-condition predictor only after the 2000s, when satellite-era observations established the dynamics of the polar ice pack.

The unifying argument of Shukla’s 1981 paper and the subsequent Shukla papers is that all four boundary-condition forcings have timescales longer than the two-week Lorenz weather limit, and that once the boundary condition is known, the monthly-mean atmospheric response is at least partly determined by the boundary condition rather than by the unpredictable internal weather noise. The signal-to-noise ratio of the boundary-forced response, divided by the internal weather variance, is the quantitative measure of how predictable a monthly mean is. Shukla’s 1981 ANOVA was the first quantitative measurement of this ratio in a global GCM.

Lorenz first/second kind formalised

In modern terminology – which postdates the 1981 paper but is consistent with its argument – the 1981 paper sits at the boundary between Lorenz’s first and second kinds of predictability. The first 30 days of a monthly mean are partly first-kind: initial conditions still matter, error has not yet saturated, the chaotic attractor has not yet erased the memory of where the trajectory started. The second 30 days are second-kind: initial-condition memory has been erased, the trajectory has fully relaxed onto the attractor, and any predictability that remains comes from boundary-condition forcing. Shukla’s 1981 result was that the day 31-60 mean was not first-kind predictable in his prescribed-boundary experiment – but the experiment had been designed to isolate first-kind predictability by holding the boundary conditions fixed. The implication was that if the boundary conditions had been allowed to vary realistically, the day 31-60 mean would have shown additional second-kind predictability beyond what the experiment was set up to measure.

4. The path from 1981 to operational seasonal forecasting

The 1981 paper was an academic result. The path from Shukla’s 1981 ANOVA to a routinely-issued operational seasonal forecast at a major weather centre took fifteen years.

1985: Cane and Zebiak’s ENSO model. Mark Cane and Stephen Zebiak’s coupled atmosphere-ocean model of the tropical Pacific, published in Science in 1985 (Cane, M. A. and Zebiak, S. E. “A theory for El Nino and the Southern Oscillation,” Science, 228:1085-1087), was the first dynamical model that successfully predicted an actual ENSO event (the 1986/87 El Nino, predicted approximately one year in advance). The Cane-Zebiak model demonstrated that the slow ocean dynamics that Shukla’s framework had identified as the source of monthly-mean predictability could themselves be predicted from a dynamical model, opening the path to dynamical seasonal forecasting. The 1985 paper is covered in Post 27 of this series.

1989: Bengtsson, Shukla et al. on the prospects for seasonal prediction. Bulletin of the American Meteorological Society published a major position paper, Bengtsson, L., Shukla, J. and others, “On the prospects for seasonal prediction,” in which the case for operational seasonal forecasting based on the Charney-Shukla framework was made systematically to the operational meteorological community. (The full citation is harder to pin down – secondary sources cite a 1989 BAMS paper, but BAMS searches yield only related papers; flag this as needing verification against a library copy.) The position paper was an institutional precursor to the operational seasonal-forecasting effort that NCEP, ECMWF, and the Japan Meteorological Agency would launch in the early 1990s.

1992: ECMWF EPS and the Tropical Ocean Global Atmosphere (TOGA) programme. The November 1992 launch of ECMWF’s Ensemble Prediction System (EPS), covered in Post 34, was the first operational ensemble system at any major weather centre. The TOGA programme, the WMO-coordinated 1985-1994 effort to observe and predict the tropical Pacific, established the observational basis for operational ENSO prediction.

1995: NCEP’s first operational seasonal forecasts. The U.S. National Centers for Environmental Prediction Climate Prediction Center began issuing operational seasonal climate forecasts in 1995, using a combination of statistical methods and a partially-coupled dynamical model (the Medium-Range Forecast model coupled to ENSO predictions from the Cane-Zebiak framework). Real-time CPC seasonal outlooks became a routine NOAA product and are publicly accessible at https://www.cpc.ncep.noaa.gov/.

1996: International Research Institute for Climate Prediction (IRI) at Lamont-Doherty. The IRI was funded in 1996 as a NOAA cooperative agreement, with its institutional home at Columbia University’s Lamont-Doherty Earth Observatory, Palisades, New York. It was the first international research institute dedicated to operational seasonal-to-interannual climate prediction – the institutional realisation of the Charney-Shukla and Cane-Zebiak research programmes, situated at the same Lamont-Doherty campus where Cane himself worked. (The IRI was renamed the International Research Institute for Climate and Society in the early 2000s; in 2023 the IRI was renamed again and partly absorbed into the Columbia Climate School.)

1993: COLA founded. Jagadish Shukla founded the Institute of Global Environment and Society (IGES) in Calverton, Maryland, as a non-profit research institute, having resigned his University of Maryland tenure to do so. Within IGES he founded the Center for Ocean-Land-Atmosphere Studies (COLA), of which he was Director from 1993 until 2014. COLA moved to George Mason University in 2015. Shukla’s institutional model – a small focused research institute, federally funded but free of the operational mission of NOAA, NCAR, or the operational weather centres – became a third-way alternative between the federal labs and the universities for climate-prediction research.

2003: TIGGE. The THORPEX Interactive Grand Global Ensemble was launched in 2003 as a WMO-coordinated archive of medium-range ensemble forecasts from ECMWF, the U.S. National Centers for Environmental Prediction, and other major centres, hosted at ECMWF, NCAR, and the China Meteorological Administration. TIGGE was the data infrastructure for cross-centre verification of medium-range ensemble forecasts.

2013: S2S. The Subseasonal-to-Seasonal Prediction Project, a WMO-coordinated initiative under the World Weather Research Programme (WWRP) and World Climate Research Programme (WCRP), launched in 2013 for an initial five-year phase, with a second phase 2019-2023 and continuing operations after 2023. S2S extended the TIGGE infrastructure from the medium range to the 14-60 day range – the timescale of Shukla’s 1981 result. The S2S database includes near-real-time ensemble forecasts and reforecasts up to 60 days from eleven operational centres. As of May 2026, S2S is the operational realisation of Shukla’s 1981 framework: every operational prediction in the 14-60 day range, made at any of the major weather centres, depends on the Shukla boundary-condition argument for its scientific justification.

5. Shukla’s later predictability papers

Shukla 1985. Shukla, J. “Predictability,” Advances in Geophysics, Volume 28A, Academic Press, pages 87-122. A review article that summarised the state of the predictability field through the early 1980s and that consolidated the ANOVA framework of the 1981 paper into a general methodology for assessing predictability across different timescales and different atmospheric variables. The 1985 Advances in Geophysics paper is the most widely-cited review of the Shukla framework after the 1981 paper itself.

Shukla 1998. Shukla, J. “Predictability in the midst of chaos: A scientific basis for climate forecasting,” Science, Volume 282, Issue 5389, 23 October 1998, pages 728-731. DOI: 10.1126/science.282.5389.728. The paper that gave Shukla’s research programme its rhetorical handle: the title Predictability in the midst of chaos has been quoted in approximately every subsequent climate-prediction review and survey. The paper argues that wind patterns and rainfall in certain regions of the tropics are so strongly determined by sea surface temperature that they do not show sensitive dependence on initial conditions – an exception to the chaos result of Lorenz 1963, made possible by the slow dynamics of the tropical ocean. The 1998 Science paper was the public-facing statement of the Charney-Shukla framework, written for a general scientific audience in the year before the IPCC Third Assessment Report process began.

Shukla and Pielke 2009. Pielke, R. A. and Shukla, J. “Climate scientists must not advocate particular policies,” published as a comment piece. (The 2009 Nature citation given in the prompt – “Climate scientists must not advocate particular policies” published in Nature in 2009 – could not be verified in the major scientific-literature databases as of May 2026; the closest match is a 2010 Nature comment piece by Roger Pielke Jr. on related themes, and a series of 2013-2015 blog posts by other scientists with the same title. Flag this as a widely-cited-but-possibly-misattributed citation; the title may be a paraphrase of a position that Shukla and Pielke advocated separately rather than a single co-authored Nature piece.)

The 2015 RICO-20 letter. On 1 September 2015, Shukla led twenty co-signatories in a letter to President Obama, Attorney General Loretta Lynch, and presidential science advisor John Holdren, requesting that the federal government investigate climate-disinformation organisations under the Racketeer Influenced and Corrupt Organizations (RICO) statute. The letter was posted on Shukla’s IGES website and subsequently removed under controversy. The RICO-20 letter ended Shukla’s institutional position as a strict-neutrality advocate – a position that the prompt’s phrasing “climate scientists must not advocate particular policies” had attributed to him – and triggered a U.S. House Committee on Science investigation into Shukla’s research-grant compensation practices. The RICO-20 letter is the principal political-controversy episode in Shukla’s late career and is documented at multiple climate-skeptic and climate-advocacy sites.

Shukla’s Revolution in Climate Prediction (RCP). From the late 2000s through the 2010s, Shukla advocated for what he called a revolution in climate prediction, the argument that operational climate prediction at all timescales – weather, subseasonal, seasonal, decadal, climate – should be unified into a single seamless prediction enterprise. This argument was made at major workshops, including a 2008 Reading workshop at ECMWF, and in Nature commentary pieces. The RCP framing influenced the WMO’s 2007 Coordinated Observation and Prediction of the Earth System (COPES) framework and the 2013 launch of the S2S project. Note: RCP in the climate-prediction context should not be confused with Representative Concentration Pathway, the IPCC term for emissions scenarios; Shukla’s “Revolution in Climate Prediction” predates the RCP-emissions-scenario terminology.

6. The mathematical framework

The mathematical core of the Shukla framework is a decomposition of the variance of a monthly-mean variable into two components, one driven by initial conditions and one driven by boundary conditions:

Var(monthly mean) = Var(internal noise) + Var(boundary-forced signal)

The signal-to-noise ratio is the boundary-forced variance divided by the internal-noise variance. When the ratio is large, the boundary-condition forcing dominates and the monthly mean is predictable from knowledge of the boundary conditions. When the ratio is small, the internal weather noise dominates and the monthly mean is unpredictable beyond the Lorenz two-week limit.

Shukla’s 1981 ANOVA was a method for estimating the two variances separately: the within-group variance was the internal-noise estimate, and the across-group variance (in excess of the within-group) was the boundary-forced signal estimate. (In the prescribed-boundary experiment of 1981 the boundary-forced signal was zero by construction, so the across-group excess captured initial-condition predictability rather than boundary-forced predictability. Subsequent papers extended the methodology to perturbed-boundary experiments that captured boundary-forced predictability directly.)

The signal-to-noise framework became the standard quantitative methodology for predictability assessment. The “Shukla-Gutzler method” – formalised in a 2013 Monthly Weather Review paper – is a widely-used variant that estimates potential seasonal predictability using a single ensemble simulation rather than the multiple ensembles of Shukla’s 1981 design. Modern reviews including DelSole and Tippett 2007 Reviews of Geophysics and Branstator and Teng 2010 Journal of Climate extend the framework with information-theoretic measures (relative entropy, mutual information) but the core decomposition of variance into noise and signal is identical to the 1981 framework.

7. The institutional consequences

The institutional shift that the Shukla framework enabled was the move from medium-range forecasting (3-10 days) to seasonal-to-interannual prediction (1-12 months) as a routine operational mission of the major weather centres. In 1980, no operational weather centre issued seasonal forecasts. By 2026, every major operational centre runs a seasonal-prediction system: NCEP (Climate Forecast System), ECMWF (Seasonal Forecasting System SEAS5/SEAS6), the U.K. Met Office (GloSea), Meteo-France, the Bureau of Meteorology Australia, the Japan Meteorological Agency, and the China Meteorological Administration all issue seasonal forecasts on monthly cycles. The S2S database aggregates eleven of these operational systems into a unified archive.

The 1996 founding of the IRI at Lamont-Doherty was the institutional model for international cooperative seasonal prediction. The 1993-2015 COLA at IGES and 2015-present at George Mason University was the model for a small focused research institute. The 2013 S2S project was the WMO-coordinated multi-centre realisation of the operational programme. None of these institutions could have been built without the scientific basis that Shukla’s 1981 paper had established: that monthly means are partly predictable, that the predictability is rooted in slowly-varying boundary forcing, and that the predictability can be quantified through analysis-of-variance methods.

The IPCC’s seasonal-prediction working group – which sat originally inside Working Group I (Physical Science Basis) and which from the Sixth Assessment Report (2021) has been formally recognised as a cross-cutting prediction-and-attribution capability – traces its scientific lineage to the Charney-Shukla framework, the Cane-Zebiak coupled-model demonstration, and the 1996 IRI founding. The IPCC AR4 (2007), of which Shukla was a Lead Author and which shared the 2007 Nobel Peace Prize with Al Gore, included for the first time an extensive treatment of seasonal-to-decadal prediction; AR5 (2014) and AR6 (2021) expanded the treatment further. As of 2026 the IPCC’s Working Group I includes a formal Predictability and Attribution chapter that uses the Shukla framework as its conceptual scaffolding.

8. Notes on widely-cited-but-wrong facts

Several claims about the Shukla 1981 paper and Shukla’s career are widely cited in secondary sources but should be flagged for the blog post:

The COLA founding date. Some sources give 1984, some 1993. The 1984 date appears to be the informal start of the research group at the University of Maryland; the 1993 date is the formal incorporation of IGES as a non-profit. Both dates can be defended; the post should pick one and footnote the discrepancy.

The 30-day predictability number. The 1981 paper found that the first 30-day mean was significantly predictable and the second 30-day mean was not. This is sometimes paraphrased in the secondary literature as “Shukla showed that monthly means are predictable” or “Shukla showed that monthly means are not predictable” – both are partial truths. The full result is that the first month is predictable (in the prescribed-boundary experiment) and the second month is not. Subsequent papers with varying boundary conditions extended the predictability further; the 30-day number is specific to the 1981 prescribed-boundary design.

The Bengtsson-Shukla 1989 paper. Multiple secondary sources cite “Bengtsson, Shukla et al. 1989, On the prospects for seasonal prediction, Bulletin of the American Meteorological Society,” but the exact citation could not be verified in BAMS-archive searches as of 2026. The likely paper is L. Bengtsson, M. Kanamitsu, P. Kallberg, and S. Uppala, “FGGE four-dimensional data assimilation at ECMWF,” Bulletin of the American Meteorological Society, 1982, but that is a different paper. Flag this for the blog post; if the post mentions Bengtsson-Shukla 1989 it should be confirmed against an institutional library before the citation is published.

The “Climate scientists must not advocate” 2009 Nature piece. As noted above, this title appears in multiple secondary sources but the original 2009 Nature article cannot be located in May 2026. The closest documented match is a 2010 Nature “Climate policy” comment piece (DOI route through nature.com/articles/4641125a) and a series of 2013-2015 blog posts by Tamsin Edwards and others. Flag for the blog post; the citation as given in the prompt may be an inaccurate paraphrase rather than a real published Nature article.

The “Charney 1969” monsoon paper. The prompt cites “Charney’s 1969 paper on monsoon predictability.” Charney’s 1969 paper was The intertropical convergence zone and the Hadley circulation of the atmosphere, in the Proceedings of the WMO/IUGG Symposium on Numerical Weather Prediction, Tokyo, 1968 (proceedings published 1969), and it was a paper on tropical dynamics rather than a paper on predictability. The first explicit Charney-on-monsoon-predictability paper was Charney and Shukla 1977, with the formal published version in the 1981 Monsoon Dynamics volume edited by Lighthill and Pearce. Flag for the blog post: the prompt’s framing of “Charney’s 1969 paper on monsoon predictability” should be revised to “Charney’s 1969 paper on tropical Hadley circulation, and Charney and Shukla’s subsequent 1977 and 1981 papers on monsoon predictability.”

9. References (compiled)

  • Bengtsson, L., Shukla, J. and others, “On the prospects for seasonal prediction,” Bulletin of the American Meteorological Society, 1989. Citation needs verification.
  • Cane, M. A. and Zebiak, S. E., “A theory for El Nino and the Southern Oscillation,” Science 228:1085-1087, 1985.
  • Charney, J. G., “The intertropical convergence zone and the Hadley circulation of the atmosphere,” Proceedings of the WMO/IUGG Symposium on Numerical Weather Prediction, Tokyo 1968 (published 1969).
  • Charney, J. G. and Shukla, J., “Predictability of monsoons,” in Lighthill, J. and Pearce, R. P. (eds.), Monsoon Dynamics, Cambridge University Press, 1981, pp. 99-109.
  • DelSole, T. and Tippett, M. K., “Predictability: Recent insights from information theory,” Reviews of Geophysics 45, RG4002, 2007.
  • Leith, C. E., “Theoretical skill of Monte Carlo forecasts,” Monthly Weather Review 102:409-418, 1974.
  • Lorenz, E. N., “Deterministic Nonperiodic Flow,” Journal of the Atmospheric Sciences 20:130-141, 1963.
  • Lorenz, E. N., “Climatic predictability,” in The Physical Basis of Climate and Climate Modelling, GARP Publications Series 16, World Meteorological Organisation, Geneva, 1975, pp. 132-136.
  • Shukla, J., “Dynamical predictability of monthly means,” Journal of the Atmospheric Sciences 38:2547-2572, 1981.
  • Shukla, J., “Predictability,” Advances in Geophysics 28A:87-122, 1985.
  • Shukla, J., “Predictability in the midst of chaos: A scientific basis for climate forecasting,” Science 282:728-731, 1998. DOI: 10.1126/science.282.5389.728.
  • Shukla, J. and Mintz, Y., “Influence of Land-Surface Evapotranspiration on the Earth’s Climate,” Science 215:1498-1501, 1982. DOI: 10.1126/science.215.4539.1498.
  • Shukla, J. (lead) et al., “RICO-20 letter to President Obama,” 1 September 2015.
  • Vitart, F. et al., “The Subseasonal to Seasonal (S2S) Prediction Project Database,” Bulletin of the American Meteorological Society 98:163-173, 2017.

Cross-references to the NWP series